This preview shows pages 1–2. Sign up to view the full content.
ORIE 3500/5500 – Engineering Probability and Statistics II
Fall 2010
Assignment 1
Problem 1
We toss a coin 3 times. For this experiment we choose
the sample space
Ω =
±
HHH,THH,HTH,HHT,TTH,THT,HTT,TTT
²
,
where
T
stands for tails and
H
stands for heads.
a.
Write down the outcomes comprising the following events:
A
:
“we throw tails exactly twice”;
B
:
“we throw tails at least twice”;
C
:
“tails did not appear
before
a head appeared”;
D
:
“the ﬁrst throw results in tails”
.
b.
Write down the outcomes comprising the following events:
A
c
,
A
∪
(
C
∩
D
),
A
∩
D
c
.
Problem 2
For events
A
and
B
, it is known that
P
(
A
) =
.
6
, P
(
B
) =
.
7 but
P
(
A
∩
B
) is unknown. What are the smallest and the largest
value that
P
(
A
∩
B
) may take?
Problem 3
A town has 4 plumbers. If 4 houses have plumbing
problems on a given day, what is the probability that exactly
i
plumbers
are called, for
i
= 1
,
2
,
3
,
4. Explain what assumptions, if any, you are
making.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/03/2010 for the course OR 3500 taught by Professor Samorodnitsky during the Fall '09 term at Cornell University (Engineering School).
 Fall '09
 SAMORODNITSKY

Click to edit the document details